There is a way to send emails from a button. I don't know if this is the best option or exactly what you need but I can send emails by adding a button in the object I need to send the email from just by using this url:
This is for the Case object but you can use it for the Task as well.
- Got to Set up
- Activities -> Task Buttons, Links and Actions
- Click in New Button or Link
- Insert label name, select Detail Page Button
- Behavior = Display in a new window
- Content Source = URL
- Insert this:
The last part of this link needs to point out to the email template you want to use for your email, so change the "template_id=00X58000000sJE3" to your template id. If you want to use this link in another button for another object you can do that by changing the parts in which you see "Task" for the object you want to use.
I have tested this on the case and opportunity objects and works fine.
Let me know if it is also working for you.
Don't forget to add you new button to your custom button section in the pages you need to.
Good luck and let us know the outcome.